Oliver Kolb

Combination of Nonlinear and Linear Optimization of Transient Gas Networks

In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed-integer nonlinear program. This is solved by means of a combination of (i) a novel mixed-integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program applied for given combinatorial constraints. Numerical experiments show that better approximations to the optimal control problem can be obtained by using solutions of the sequential quadratic programming algorithm to improve the mixed-integer linear program. Moreover, iteratively applying these two techniques improves the results even further.

Mixed integer linear models for the optimization of dynamical transport networks

We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability.

Speed limit and ramp meter control for traffic flow networks

The control of traffic flow can be related to different applications. In this work, a method to manage variable speed limits combined with coordinated ramp metering within the framework of the Lighthill–Whitham–Richards (LWR) network model is introduced. Following a ‘first-discretize-then-optimize’ approach, the first order optimality system is derived and the switch of speeds at certain fixed points in time is explained, together with the boundary control for the ramp metering. Sequential quadratic programming methods are used to solve the control problem numerically. For application purposes, experimental setups are presented wherein variable speed limits are used as a traffic guidance system to avoid traffic jams on highway interchanges and on-ramps.

On the Full and Global Accuracy of a Compact Third Order WENO Scheme

Recently, Arandiga et al. showed in [SIAM J. Numer. Anal., 49 (2011), pp. 893--915] for a class of weighted ENO (WENO) schemes that the parameter

An implicit box scheme for subsonic compressible flow with dissipative source term

\varepsilon

Hierarchical Modelling and Model Adaptivity for Gas Flow on Networks

occurring in the smoothness indicators of the scheme should be chosen proportional to the square of the mesh size,

Optimization for a special class of traffic flow models: Combinatorial and continuous approaches

h^2

An adaptive model switching and discretization algorithm for gas flow on networks

, to achieve the optimal order of accuracy. Unfortunately, these results cannot be applied to the compact third order WENO reconstruction procedure introduced in [D. Levy, G. Puppo, and G. Russo, SIAM J. Sci. Comput., 22 (2000), pp. 656--672], which we apply within the semidiscrete central scheme of [A. Kurganov and D. Levy, SIAM J. Sci. Comput., 22 (2000), pp. 1461--1488], a commonly used scheme for the numerical solution of conservation laws and convection-diffusion equations. The aim of this paper is to close this gap. In particular, we will show that we achieve the optimal order of accuracy in the WENO reconstruction (

A continuous buffer allocation model using stochastic processes

h^3

Simulation and Continuous Optimization

in the smooth case and